Scale of Curve to effect Location of "Set of objects"
Circular Path
If the shape of the curve is a circle, this can be achieved even without a curve.  You just need a few empties placed in correct positions (around the circle) and parented to some object whose Scale will be adjusted to move the visible objects (Cube in my example)


When the circle is scaled, each empty moves as if they are parented to a certain location on the (circular) curve.  But in fact this is just simple parent transformation.

Instead of parenting the cube to an empty, we can just copy its location using Copy Location constraint.
Non-Circular Path

A more generalized solution is to use a Follow Path constrains on the visible objects and constrain them to the curve directly.
Important thing here is to give each visible object a difference offset (on the curve). If we have 6 objects, for example, each one should have an offset 100 / 6 * i (where i is the index of the object, 0, 1, 2, ...).

This method should work on any kind of curve, open or closed.